Okay, this is the result of a bit of time thinking about a picture where a woman remarks that she wishes there were more strong female characters in gaming. The comic itself lists the following women or games as examples (Spoiler Tagged to cut down on size):
The majority of Resident Evil characters, Bayonetta, Faith from Mirror's Edge, Lightning from FFXIII, Parasite Eve, Chun-Li, Samus, Fatal Frame protagonists, SH3's Heather, Dreamfall, any RPG with character creation (you are whatever you want to be, doing whatever you want), Alice of American McGee, TouHou, Zoey and Rochelle from Left 4 Dead, Jade from Beyond Good and Evil, Kaine (who's techncially herm? but notable), Curly Brace from Cave Story, Borderland's women, Monohime from Muramasa....Chelle from Portal (heck Glad0s too), Recette, Joanna Dark from Perfect Dark, Lara Croft, Shepard (can be either male or female, and there are strong female roles in that game too), Amaterasu....
And THEN...I got thinking...and then I came up with my list...
Quistis, Terra, Tifa, Dagger/Garnet Yuna comes into her own (ignoring X-2 for silly outfits), Main Villains in 8 were women sorceresses, 7 had a female chocobo manager, Aerith wasn't afraid to die to save the world, Yuffie was looking for independence from her princess heritage, Elena holds a position among the Turks (who are a Black-Ops task group for Shin-Ra), Scarlet runs the Weapons Division of Shin-Ra...Wild Arms had Cecilia, a princess come into her own by cutting off her hair and choosing freedom and independence over conformity, and an NPC named Calamity Jane (who turns PC in the remake with ANOTHER female NPC genius named Emma, a scientist with awesome abilities) who's independent herself...main boss demon was a woman, one of the best swordswomen in the world was a woman...WA2 had Kanon and Lilka and Marivel coming to terms with their past and becoming stronger characters, Antenora used the leader of the terrorist group Odessa to hurt his heart as much as he had wronged her life...the legendary hero of old who took on the worst threat to life on Filgaia was just an ordinary woman who had taken up a sword to protect life...Wild Arms 3 had a coming of age story as well, with a female rivalry helping Virginia understand how to survive and lead her group...final boss was a girl....
FFXI had plenty of female characters in positions of power, from the Tarus to the Elvaan...one of the best thieves around is a Mithra woman...Ellie from The Last of Us has to become strong and help a fully-grown man survive a near-fatal injury... as a kid...Legend of Dragoon has a woman save your ass FROM A DRAGON within the first three minutes...Chrono Cross has Kid, Chrono Trigger has Lucca as a genius, Marle is a princess who will shoot you in the face with a crossbow...Ayla is a bit sexualized, but still a strong fighter from a period of primitive humans...Elizabeth from Bioshock Infinite undergoes an arc, the leader of the Vox Populi is a woman, Tenenbaum from Bioshock 1.
You really need Cortana in order to do a lot of things in Halo cause Master Chief isn't exactly a master hacker. Chun-Li is strong, but you could argue Cammy, Rose, Juri, Viper, Ibuki, Sakura, and Makoto all have strong characters...most fighting game rosters have strong women. Then there's Meryl and Naomi from Metal Gear Solid...Sniper Wolf...Fortune...EVA and The Boss...
Coco from Crash Bandicoot is depicted as an intelligent hacker...Mona Sax from Max Payne, twice over...main villain from that game was a woman running a large corporation...
Indie games have them too. Bandage Girl subverts the kidnapping trope at the end by kicking the crap out of Dr. Fetus. Iji has your protagonist as a teenage woman standing up for the remnants of humanity that survived, and you can choose to be a pacifist or fight for your right...there's a lesbian couple for one alien race, and the other alien race has one that's nigh indestructible and another that's a highly trained assassin. Knytt Stories features Juni, who's a veritable ninja. Ib has plenty of emotion without having to say a word. Witch's House has two female leads in it as well. Yume Nikki has a metric ton of symbolism in it, telling much about Madotsuki's life and relationships with the world around her.
You could argue in some cases they aren't the protagonists or lead role, but they're still strong characters.
That was just me going off the cuff. I'm pretty sure I could dig even further. So I wanna throw this out there, cause I wanna see how deep this rabbit hole actually goes: Can you name your own personal list of female characters (well-written, strong, prominent, or otherwise) that you know of?